add set stuffs

sets.rkt

@@ -0,0 +1,146 @@
+#lang racket
+;
+;(define (element-of-set? x set)
+;  (cond ((null? set) #f)
+;        ((equal? x (car set)) #t)
+;        (else (element-of-set? x (cdr set)))))
+;
+;(define (adjoin-set x set)
+;  (if (element-of-set? x set)
+;      set
+;      (cons x set)))
+;
+;(define (intersection-set set1 set2)
+;  (cond ((or (null? set1) (null? set2)) 
+;         '())
+;        ((element-of-set? (car set1) set2)
+;         (cons (car set1)
+;               (intersection-set (cdr set1) 
+;                                 set2)))
+;        (else (intersection-set (cdr set1) 
+;                                set2))))
+;
+;(define (union-set set1 set2)
+;  (cond ((null? set1)set2)        
+;        ((element-of-set? (car set1) set2)
+;         (union-set (cdr set1) set2))
+;        (else (cons (car set1)
+;                    (union-set (cdr set1)
+;                                      set2)))))
+;(element-of-set? 1 '(1 2 3))
+;(union-set '(10 3 5)'(1 2 3))
+
+(define set1 '(4 9 8 6 43 4))
+(define set2 '(10 6 4 89 2 3 5 43 4))
+;9 8 10 6 4 89 2 5 43 4
+(define (element-of-set?* x set)
+  (cond ((null? set) #f)
+        ((equal? x (car set)) #t)
+        (else (element-of-set?* x (cdr set)))))
+
+(element-of-set?* 4 '(9 8 6 43 4 4))
+;O(n) but potential worse due to more elements
+(define (adjoin-set* x set)
+  (cons x set))
+;O(1) vs O(n)
+(adjoin-set* 5 set1)
+
+(define (intersection-set* set1 set2)
+  (cond((or(null? set1)(null? set2))
+        '())
+       ((element-of-set?* (car set1) set2)
+        (cons (car set1)
+              (intersection-set* (cdr set1)
+                                 set2)))
+       (else (intersection-set* (cdr set1)
+                                set2))))
+(intersection-set* set1 set2)
+;O(n^2)
+(define(union-set* set1 set2)
+  (append set1 set2))
+(union-set* set1 set2)
+;O(n)
+
+(define (adjoin-set x set)
+  (cond((null? set)(list x))
+       ((< x (car set))(cons x set))
+       ((= x (car set))set)
+       (else (cons (car set)(adjoin-set x (cdr set))))))
+(displayln "test adjoin-set") 
+(adjoin-set 3 '(1 2 4))
+(adjoin-set 3 '(1 2 5))
+(adjoin-set 6 '(1 2 5))
+(adjoin-set 1 '(1 2 5))
+(adjoin-set 1 '(2 3 4))
+(adjoin-set 2 '(2 3 4))
+(adjoin-set 1 '(3 4 5))
+(adjoin-set 2 '(3 4 5))
+(adjoin-set 2 '())
+
+;(define (union-set set1 set2)
+;  (cond((null? set1)set2)
+;       (else (union-set (cdr set1)(adjoin-set (car set1)set2)))))
+;still O(n^2) just slightly better
+
+
+;(define (union-set set1 set2)
+;  (if
+;   (let ((x1 (car set1))(x2 (car set2)))
+;     (cond((= x1 x2)
+;           (cons x1 (union-set (cdr set1)(cdr set2))))
+;          ((and(< x1 x2)(or(null? (cdr set1))(< x2 (cadr set2))))
+;           (cons x1 (cons x2 (union-set (cdr set1)(cdr)
+
+(define (union-set set1 set2)
+  (cond((null? set1)set2)
+       ((null? set2)set1)
+       (else
+        (let ((x1 (car set1))(x2 (car set2)))
+          (cond((= x1 x2)
+                (cons x1 (union-set (cdr set1)(cdr set2))))
+               ((and(< x1 x2))
+                (cons x1 (union-set (cdr set1) set2)))
+               ((and(> x1 x2))
+                (cons x2 (union-set set1 (cdr set2)))))))))
+
+(displayln "test union-set")                                        
+(union-set '(1 3 5 8)'(2 4 6 7))
+(union-set '(1 3 5)'(1 2 3 4 5 6))
+(union-set '(1 2 3 4 5 6)'(2 4 6))
+(union-set '(1 2 3)'(4 5 6))
+(union-set '(2 3 4 5 6)'(1 2 3 7))
+
+(define (disjoin set1 set2)
+  ;numbers that are not in both sets
+  (cond((null? set1)set2)
+       ((null? set2)set1)
+       (else
+        (let((x1 (car set1))(x2 (car set2)))
+          (cond((= x1 x2)
+               (disjoin (cdr set1)(cdr set2)))
+               ((< x1 x2)
+                (cons x1(disjoin(cdr set1)set2)))
+               (else(cons x2(disjoin set1 (cdr set2)))))))))
+
+(disjoin '(1 2 3)'(1 3 4))
+(disjoin '(1 2 3 6)'(1 3 4))
+(disjoin '(1 2 3 6)'(1 3 4 5 7))
+
+(define(difference set1 set2)
+    ;only the numbers from the first set not in the second
+    (cond((null? set1)'())
+       ((null? set2)set1)
+       (else
+        (let((x1 (car set1))(x2 (car set2)))
+          (cond((= x1 x2)
+               (difference (cdr set1)(cdr set2)))
+               ((< x1 x2)
+                (cons x1(difference(cdr set1)set2)))
+               (else(difference set1 (cdr set2))))))))
+(difference '(1 2 3)'(1 3 4))
+(difference '(1 2 3 6)'(1 3 4))
+(difference '(1 2 3 5 6)'(1 3 4 5 7))
+(difference '(1 2 3 5 6 7)'(1 3 4 7))
+(append '() (list 1) '() (list 2))
+
+